I was drawn to this chapter in our textbook in part because of an interest I have in 3D computer modeling. Polygon modeling is one way of creating 3D objects with software such as Maya and 3D Studio Max. The creation and manipulation of polygon vertices, edges and faces through rotation, positioning and scaling is one way of building characters and objects for movies and games. This paper starts with definitions of basic terminology related to the subject of polygons, tiling with the pentagon in particular.

A polygon is a shape that can be drawn on a plane (a 2 dimensional surface) so that the starting and ending points are the same and the path never crosses or retraces itself. We will call the line segments that compose a polygon sides, and the end points of the sides, vertices. Polygons  include the triangle(3 sides), Quadrilateral (4 sides),Pentagon (5 sides),and  Hexagon (six sides), there are many more and as the number of sides increase they are often refered to simply as N-gons.

If you can cover an entire plane with a polygon shape so that no gaps exist, it is said to be tileable. A Regular Polygon has sides that are all of equal length, and the angles at each vertex are all of the same degree. The square and the equilateral triangle are 2 examples of Regular Polygons. An irregular Polygon has side lengths and vertex angles that are not all identical.

An edge to edge tiling is one in which polygons tile a plane without gaps and the entire length of a polgon’s edge is matched by the edge of another polygon. A good example of a tileable pattern that is not edge to edge is a […]